Consider the recurrence relation with ao 1, a =1, a2 = 3. (a) Calculate an for...

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Consider the recurrence relation with ao 1, a₁ =1, a2 = 3. (a) Calculate an for n ≤ 6. (b) Prove that the generating function an+3 = 3an+1 - 2an A(x) = Σ n>0 anxn = 1 + x (1-x)²(1 + 2x) (c) Use a partial fraction expansion of A(x) to find an explicit expression for an. Consider the recurrence relation with ao 1, a₁ =1, a2 = 3. (a) Calculate an for n ≤ 6. (b) Prove that the generating function an+3 = 3an+1 - 2an A(x) = Σ n>0 anxn = 1 + x (1-x)²(1 + 2x) (c) Use a partial fraction expansion of A(x) to find an explicit expression for an.

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a Here are the steps to calculate an for n 6 a0 1 a1 1 a2 3 a3 3a1 2a0 31 21 3 a4 ... View the full answer